Normalized null hypersurface in Lorentzian mani- folds admitting a conformal vector field

Abstract

In this paper, we study the geometry of null hypersurface in Lorentzian manifolds furnished with a conformal vector field W with special attention paid to conformally stationary spacetime. We prove that an Einstein null hypersurface in Lorentzian manifolds of quasi-constant curvature for which the closed conformal rigging vector field is a curvature vector field, is locally a product of null curves, Euclidean spaces, and spheres.